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I am trying to evaluate the right hand side of the following equation and then rearrange the whole thing in terms of x.

Q=xT+3x*Integral(1-e^(b*t)dt 

The integral has a lower limit of 0 and an upper limit of T. Here is what I keep getting when I evaluate the r.h.s

3 (1 - E^-[b]t) T x + xT

Is my evaluation of the r.h.s accurate? Also, How do I rearrange everything interms x? From what I have read so far, it looks like I have to use Solve and Reduce. I would appreciate any help I can get.

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    $\begingroup$ Can you please include the Mathematica code you are evaluating. Just a guess based on the information provided x T + 3 x Integrate[1 - e^(b*t), {t, 0, T}] = T x + 3 x (T + (1 - e^(b T))/(b Log[e])) Which is easy to rearrange in terms of x. $\endgroup$ – Rohit Namjoshi Sep 11 '18 at 4:24
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After correcting several syntax errors and useing Solve:

x /. Solve[y == x T + 3 x*Integrate[1 - E^(b*t), {t, 0, T}], x][[1]]

$$\frac{b y}{4 b T-3 e^{b T}+3}$$

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